# How do you factor n^4 - 1?

Dec 17, 2015

$\left(n - 1\right) \left(n + 1\right) \left({n}^{2} + 1\right)$

#### Explanation:

By using this formula ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

here we have $a = {n}^{2}$ and $b = 1$

${\left({n}^{2}\right)}^{2} - 1$ (remember ${\left({a}^{n}\right)}^{m} = {a}^{n m}$)

$\left({n}^{2} - 1\right) \left({n}^{2} + 1\right)$

You do it again with $\left({n}^{2} - 1\right) \left({n}^{2} + 1\right)$ and you have your answer